A collision between a comet and an asteroid named Orpheus takes place. Now the meteor Orpheus, which is five miles wide, is on a collision course with Earth. While the United States government and military engage in political maneuvering, other smaller and faster moving fragments rain down on Earth. The major plot point involves secret orbiting nuclear missile platforms, one put up by Dr. Bradley's (Connery) team for the U.S., named Hercules and another constructed by his counterpart in the Soviet Union, nicknamed Peter the Great by Dubov. The American president (Fonda) is advised by military leaders against admitting the existence of Hercules, at the same time the Soviets are reluctant to admit to the existence of its orbital weapons.

The President goes on national television and reveals the existence of Hercules, explaining it as a foresighted project to meet the threat that Orpheus represents. He also offers the Soviets a chance to save face and join in by saying they had the same foresight and have their own. Bradley requested a scientist named Dr. Alexei Dubov (Keith) to help him plan a countereffort against Orpheus.

Bradley and Sherwood have already arrived at the control center for Hercules, which is located beneath the Sony Building (then called the AT&T Building) in downtown New York. Major-General Adlon (Landau) is the commander of the facility. Dubov and his assistant (and English voice) Tatiana Donskaya (Natalie Wood) arrive and Bradley works at breaking the ice of distrust held by Hercules commander Adlon. Since Dubov cannot admit the existence of the Soviet device, he agrees to Bradley's proposal that they work on the "theoretical" application of how a "theoretical" Soviet platform's weapons would be coordinated with the American ones.

Meanwhile, further fragments of the meteor affect the Earth. The Soviets finally admit that they have the device and are willing to join in the effort. The satellite, christened Peter the Great by the joint US-Soviet team working at Hercules control, and Hercules are turned around to aim into space. On Sunday morning, Peter the Great's missiles are fired off because of its position along the orbit, Hercules is fired 40 minutes later.

Hercules is launched, and a moment later, New York is wiped out by a fragment of the meteor (one scene shows the World Trade Center destroyed in a giant fireball). Several workers inside the control center are killed when the facility is partially destroyed. The survivors slowly work their way out of what has become a trap, dealing with the East River breaking into the tunnels. Meanwhile, the two sets of missiles are linking up into three waves of mixed nationality. The Hercules crew reach a subway station filled with other people and wait while others try to dig out. The radio stations broadcast news of the result: Orpheus has been either obliterated or shifted to a harmless trajectory. Just then, the subway station occupants are rescued.

Later, the scene switches to an airport with a Soviet flag and an American flag on a hanger door. from here, Dubov and Tatiana say goodbye to Bradley and others, then they board a plane with the Soviet star and it takes off for Russia.